I am assuming you mean “Liberalism and Conservatism” when you say “left and right”
I do not, because those are not the same thing in the same way buttered toast is not a pizza. Liberalism is "centrist". It appears egalitarian at first glance, but if focuses heavily (if not entirely) on means rather than ends, allowing for (and even encouraging) consolidation of wealth & power; that is: rightward drift. "Conservatism" is a relative term, not an absolute.
Libertarianism is a patently right-leaning ideology that completely rejects authoritarianism.
Libertarianism's origins are leftist/anarchist, but the term itself has recently been co-opted by rightists and liberals the same way authoritarians always always co-opt leftist terms.
communism is state-imposed redistribution of economic means; that is 100% undeniably a left-leaning ideology that accepts and implements authoritarianism.
That is not the definition of communism. Regardless of what you think about Marxist concepts themselves (or their feasibility) Marxism/Communism requires the "withering away of the state." So long as there is entrenched leadership, that society is not leftist in the same way the Nazis were not socialist, and Republicans are not "pro-life". And yes, that means the USSR was right wing, not left. At no point did the USSR meet the criteria or definition of communism. The definitions lead to the label, not the other way around.